Spectral models (left panels) and S/N maps (right panels) of the chemical species investigated in the dayside atmosphere of TOI-2109b. The three top panels show the information for the individual chemical species Fe I, CO, and H₂O, the bottom panels show the information for all species combined. We note that the species-combined signal is dominated by the CO detection with CRIRES⁺. The Fe I spectral signature mainly stems from CARMENES, the CO signal from the CRIRES⁺ data; the investigated H₂O emission lines fall in the wavelength ranges of both instruments. The H₂O model spectrum shows particularly weak emission lines due to the predominant thermal dissociation of the species at the elevated temperatures of the TOI-2109b atmosphere. The wavelengths covered by CARMENES and the CRIRES⁺ K2166 setting used in this work are indicated by the gray shaded area. The expected position of the planetary signal in the S/N maps is indicated by the yellow dashed lines. We show the S/N maps corresponding to the optimal SYSREM iteration number as determined in Sect. 4.3.